Physically Based Modeling -Overview-

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Presentation transcript:

Physically Based Modeling -Overview- Jeong-Mo Hong Department of Computer Science Korea University

Contents Introduction Numerical Analysis Rigid Body Cloth Simulation Fluid Simulation Fluid Control

Modeling What is a model? A model is an idealized and simplified representation of reality Not always!

Motivation Can you design the movements and the reactions of 1000 rings? Guendelman et al. 2003

Physically Based Animation Problem definition How to map a natural phenomena to a computer simulation program? Mathematical modeling The description of natural phenomena by mathematical equations Differential equations that govern dynamics and geometric representation of objects Numerical simulation Computing an efficient and accurate solution of the mathematical equations Applications All the phenomena in this world!

Numerical Analysis - Introduction -

Rigid Body Equations of Motion Guendelman et al. 2003

If you want more … Topics Collision detection and response Friction

Cloth Equations of motion

If you want more, … Topics Collision detection Sensitivity Robustness

References Cloth and Rigid body Fluids Fluid control Physically Based Modeling David Baraff and Andrew Witkin ACM Siggraph Course Note Fluids Real-Time Fluid Dynamics for Games Jos Stam Proceedings of the Game Developer Conference, March 2003 Fluid control Controlling fluid animation with geometric potential Jeong-mo Hong and Chang-Hun Kim Computer Animation and Virtual Worlds, Volume 15, Issue 3-4, pp.147-157, 2004. If you want more, … Practical Animation of Liquids Foster, N. and Fedkiw, R. SIGGRAPH 2001, 15-22 (2001) Visual Simulation of Smoke Fedkiw, R., Stam, J. and Jensen, H.W. SIGGRAPH 2001, 23-30 (2001) Stable but Responsive Cloth Kwang-Jin Choi and Hyeong-Seok Ko. ACM Transactions on Graphics, Vol. 21, Issue 3, pp 604-611, 2002

추가자료

A State Vector State of an object Position and velocity State vector

Newtonian Mechanics

Euler’s Method Tayler expansion Euler’s method

Stability

Implicit Integration

Stability

Fluid Equations of motion Topics Simulation efficiency Numerical stability Object interaction More and more phenomena